The incident occurred near Bhermau village when the family was returning to Saharanpur from Patiala in Punjab in their car, Senior Superintendent of Police Nitin Tiwari said.
The victim identified as Abhitosh Kaur was killed on the spot while her father Professor Kamaljeet and mother Navneet Kaur were seriously injured, he said.
Meanwhile, the truck driver escaped from the spot leaving his vehicle behind, Tiwari said.
The body was sent for postmortem and the injured rushed to the district hospital from where they were referred to higher Centre, he said.